Question

4. Suppose we have a continuous, differentiable function \(f\) with the following properties: \(\lim_{x \to \infty} f(x) = -2\) \(\lim_{x \to -\infty} f(x) = -2\) \(f'(3) = 0\) \(f''(x) < 0\) on the interval \((1, 5)\). \(f''(x) > 0\) on the intervals \((-\infty, 1)\) and \((5, \infty)\). (a) (4 points) Sketch a possible graph of \(f\). (b) (2 points) From our given information, does \(f\) definitely have an absolute maximum? If so, where does it occur?

          4. Suppose we have a continuous, differentiable function \(f\) with the following properties:
\(\lim_{x \to \infty} f(x) = -2\)
\(\lim_{x \to -\infty} f(x) = -2\)
\(f'(3) = 0\)
\(f''(x) < 0\) on the interval \((1, 5)\).
\(f''(x) > 0\) on the intervals \((-\infty, 1)\) and \((5, \infty)\).
(a) (4 points) Sketch a possible graph of \(f\).
(b) (2 points) From our given information, does \(f\) definitely have an absolute maximum? If so, where
does it occur?

4. Suppose we have a continuous, differentiable function f with the following properties:
limx →∞ f(x) = -2
limx → -∞ f(x) = -2
f'(3) = 0
f”(x) < 0 on the interval (1, 5).
f”(x) > 0 on the intervals (-∞, 1) and (5, ∞).
(a) (4 points) Sketch a possible graph of f.
(b) (2 points) From our given information, does f definitely have an absolute maximum? If so, where
does it occur?

Added by Kenneth W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ahmet Yavas

Step 1

Since f > 0 on the intervals (-∞, 1) and (5, ∞), we know that the graph of f will be above the x-axis in these intervals. Since lim f --> 2 - f'(3) = 0, we know that the graph of f will have a horizontal tangent line at x = 3. This means that the graph of f will Show more…

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Suppose we have n continuous, differentiable function f with the following properties: - lim f --> 2 - f'(3) = 0 - f < 0 on the interval (1, 5) - f > 0 on the intervals (âˆ’âˆž, 1) and (5, âˆž) a) Sketch a possible graph of f. b) From our given information, does f definitely have an absolute maximum? If so, where does it occur?